Ensemble-averaged equations are derived for small-amplitude acoustic wave propagation through non-dilute suspensions. The equations are closed by introducing effective properties of the suspension such as the compressibility, density, viscoelasticity, heat capacity, and conductivity. These effective properties are estimated as a function of frequency, particle volume fraction, and physical properties of the individual phases using a self-consistent, effective-medium approximation. The theory is shown to be in excellent agreement with various rigorous analytical results accounting for multiparticle interactions. The theory is also shown to agree well with the experimental data on concentrated suspensions of small polystyrene particles in water obtained by Allegra & Hawley and for glass particles in water obtained in the present study.
Sangani, Ashok S.; Spelt, Peter D. M.; Norato, Michael A.; Greenwood, Margaret S.; and Tavarides, Lawrence L., "Attenuation of Sound in Concentrated Suspensions: Theory and Experiments" (2001). Biomedical and Chemical Engineering. Paper 17.